I am looking for a spline interpolation that is 3 times differentiable, strictly monotone and doesn't involve the inclusion of extra control nodes. I found this paper that describes the construction of monotone rational cubic splines in $C^2$, but I can not find any method that constructs $C^3$ splines. I don't care about the degree of the polynomial, just that it can be constructed without introducing extra points and that the monotonicity conditions are given in closed form. Is there any work you can point me to or is this an open problem?
2026-03-27 22:59:41.1774652381
$C^3$ monotone spline interpolation
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